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The difference between the maximum and minimum values of the function f x = x 3 - 3 x + 4 ,   ∀ x ∈ 0,1 is

Correct answer

2

Step-by-step solution

As, f ′ x = 3 x 2 − 3 = 3 x - 1 x + 1 Hence, f x is decreasing ∀ x ∈ 0,1 Thus, f ( x ) m a x = f 0 = 4   &   f ( x ) m i n = f 1 = 2 ∴ the required difference = 2

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